Plane strain transformation theory derives how the strain components at a point—normal strains and shearing strain referred to a rectangular reference axis system—change when expressed in terms of a second axis system rotated by an arbitrary angle, yielding closed-form transformation equations analogous to those for plane stress. From these transformation equations follow the concepts of principal strains (the extremal normal strains at a point) and principal angles (the orientations at which shearing strain vanishes and normal strain is extremal), obtained by the same mathematical structure used for principal stresses. This belongs to solid mechanics / strength of materials, specifically the theory of strain analysis, and is the strain-based counterpart to stress transformation theory within the broader study of deformation and material response under load.
Plane strain transformation theory derives how the strain components at a point—normal strains and shearing strain referred to a rectangular reference axis system—change when expressed in terms of a …